Finite Group Databasebeta

← C149×#9344 #49188293

Subgroups — C149×#9344 #49188293

Order 38144.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3193×C149C211yesmaximal, characteristic
2#2378×C149C211yesmaximal, characteristic, complemented
3#1964×C149C211yesmaximal, characteristic
4#1510×C149C211yesmaximal, characteristic
5#1508×C149C211yesmaximal, characteristic, complemented
6#1305×C149C211yesmaximal, characteristic, complemented
7#1284×C149C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C149C2211yescharacteristic
9C2×#121×C149C2211yescharacteristic
10#484×C149C412yescomplemented
11#480×C149—21no—
12#468×C149—22no—
13#450×C149C412yescomplemented
14#448×C149—21no—
15C2×#99×C149—21no—
16C2×#99×C149—21no—
17#407×C149C2211yescharacteristic
18#407×C149C2211yescharacteristic
19#391×C149—21no—
20#389×C149—21no—
21#388×C149—21no—
22#388×C149—21no—
23#387×C149—21no—
24#387×C149—21no—
25#381×C149C2211yescharacteristic
26#380×C149C2211yescharacteristic
27C4×C22⋊C4×C149C2211yescharacteristic
28#328×C149—22no—
29#327×C149—21no—
30#327×C149—21no—
31C22×Q8×C149D411yescharacteristic
32C22×D4×C149—21no—
33C22×D4×C149C2×C411yescharacteristic
34C23×C4×C149C2311yescharacteristic
35C2×SD16×C149—22no—
36C2×M16×C149—21no—
37C2×M16×C149—21no—
38C22⋊Q8×C149—21no—
39C22⋊Q8×C149—21no—
40C22⋊Q8×C149C2×C412yes—
41C22⋊Q8×C149D412yes—
42#121×C149—21no—
43#121×C149—21no—
44#121×C149—21no—
45#121×C149—21no—
46C2×C4⋊C4×C149—21no—
47C2×C4⋊C4×C149—21no—
48C2×C4⋊C4×C149—21no—
49C2×C4⋊C4×C149—21no—
50C2×C4⋊C4×C149C2×C411yescharacteristic
51C2×C4⋊C4×C149D411yescharacteristic
52C2×C22⋊C4×C149—21no—
53C2×C22⋊C4×C149—21no—
54C2×C22⋊C4×C149—21no—
55C2×C22⋊C4×C149—21no—
56C2×C22⋊C4×C149D411yescharacteristic
57C2×C22⋊C4×C149D411yescharacteristic
58C2×C42×C149—21no—
59C2×C42×C149—21no—
60C2×C42×C149—21no—
61#107×C149—22no—
62#103×C149—22no—
63#102×C149—22no—
64#99×C149—42no—
65#99×C149—42no—
66C22⋊C8×C149—21no—
67C22⋊C8×C149—21no—
68C22⋊C8×C149—21no—
69C22⋊C8×C149C2×C412yes—
70#95×C149—21no—
71#95×C149—21no—
72#95×C149—21no—
73#95×C149—21no—
74#95×C149—21no—
75#95×C149—21no—
76#95×C149—21no—
77#95×C149D411yescharacteristic
78#95×C149D411yescharacteristic
79C24×C149—21no—
80C24×C149C2×D411yescharacteristic
81C2×Q8×C149—21no—
82C2×Q8×C149—81no—
83C2×Q8×C149C22⋊C412yes—
84C2×D4×C149—21no—
85C2×D4×C149—21no—
86C2×D4×C149—41no—
87C2×D4×C149—41no—
88C2×D4×C149—41no—
89C2×D4×C149—41no—
90C2×D4×C149—41no—
91C2×D4×C149—41no—
92C2×D4×C149—81no—
93C22×C4×C149—21no—
94C22×C4×C149—21no—
95C22×C4×C149—21no—
96C22×C4×C149—21no—
97C22×C4×C149—21no—
98C22×C4×C149—21no—
99C22×C4×C149—21no—
100C22×C4×C149—41no—
101C22×C4×C149—81no—
102C22×C4×C149C22×C411yescharacteristic
103C22×C4×C149C2×D411yescharacteristic
104C22×C4×C149C2×D411yescharacteristic
105C22×C4×C149C2×D411yescharacteristic
106C22×C4×C149#4111yescharacteristic
107C22×C4×C149#4111yescharacteristic
108SD16×C149—82no—
109M16×C149—81no—
110M16×C149—81no—
111C2×C8×C149—22no—
112C2×C8×C149—41no—
113C4⋊C4×C149—22no—
114C4⋊C4×C149—22no—
115C4⋊C4×C149—21no—
116C4⋊C4×C149—21no—
117C4⋊C4×C149—21no—
118C4⋊C4×C149—81no—
119C4⋊C4×C149—81no—
120C4⋊C4×C149—81no—
121C4⋊C4×C149C22⋊C412yes—
122C22⋊C4×C149—22no—
123C22⋊C4×C149—22no—
124C22⋊C4×C149—22no—
125C22⋊C4×C149—41no—
126C22⋊C4×C149—41no—
127C22⋊C4×C149—41no—
128C22⋊C4×C149—41no—
129C22⋊C4×C149—41no—
130C22⋊C4×C149—81no—
131C42×C149—81no—
132C42×C149—81no—
133C42×C149—81no—
134C23×C149—21no—
135C23×C149—21no—
136C23×C149—41no—
137C23×C149—41no—
138C23×C149—41no—
139C23×C149—41no—
140C23×C149—41no—
141C23×C149—81no—
142C23×C149—81no—
143C23×C149C4×D411yescharacteristic
144C23×C149#12011yescharacteristic
145C23×C149#12111yescharacteristic
146Q8×C149—42no—
147Q8×C149—81no—
148D4×C149—42no—
149D4×C149—81no—
150D4×C149—81no—
151D4×C149—81no—
152D4×C149—81no—
153D4×C149—81no—
154C2×C4×C149—22no—
155C2×C4×C149—22no—
156C2×C4×C149—41no—
157C2×C4×C149—41no—
158C2×C4×C149—41no—
159C2×C4×C149—41no—
160C2×C4×C149—41no—
161C2×C4×C149—41no—
162C2×C4×C149—41no—
163C2×C4×C149—41no—
164C2×C4×C149—41no—
165C2×C4×C149—41no—
166C2×C4×C149—41no—
167C2×C4×C149—41no—
168C2×C4×C149—42no—
169C2×C4×C149—41no—
170C2×C4×C149—41no—
171C2×C4×C149—41no—
172C2×C4×C149—41no—
173C2×C4×C149—41no—
174C2×C4×C149—41no—
175C2×C4×C149—41no—
176C2×C4×C149—41no—
177C2×C4×C149—41no—
178C2×C4×C149—41no—
179C2×C4×C149—41no—
180C2×C4×C149—41no—
181C2×C4×C149—41no—
182C2×C4×C149—81no—
183C2×C4×C149—81no—
184C2×C4×C149C2×C22⋊C411yescharacteristic
185C2×C4×C149C4×D411yescharacteristic
186C2×C4×C149#12111yescharacteristic
187C2×C4×C149#12311yescharacteristic
188C8×C149—42no—
189C8×C149—81no—
190C22×C149—21no—
191C22×C149—21no—
192C22×C149—21no—
193C22×C149—21no—
194C22×C149—21no—
195C22×C149—21no—
196C22×C149—21no—
197C22×C149—21no—
198C22×C149—81no—
199C22×C149—81no—
200C22×C149—81no—
201C22×C149—81no—
202C22×C149—81no—
203C22×C149—161no—
204C22×C149—161no—
205C22×C149#38611yescharacteristic
206C22×C149#45311yescharacteristic
207C22×C149#45411yescharacteristic
208C4×C149—21no—
209C4×C149—21no—
210C4×C149—21no—
211C4×C149—21no—
212C4×C149—42no—
213C4×C149—42no—
214C4×C149—81no—
215C4×C149—81no—
216C4×C149—81no—
217C4×C149—81no—
218C4×C149—82no—
219C4×C149—81no—
220C2×C149—21no—
221C2×C149—21no—
222C2×C149—41no—
223C2×C149—41no—
224C2×C149—161no—
225C2×C149#188311yescharacteristic
226C2×C149#190511yescharacteristic
227C2×C149#191311yescharacteristic
228#9344C14911yesmaximal, characteristic, direct product factor, Sylow
229C149#934411yescharacteristic, direct product factor, Sylow
230#3193C2×C14911yescharacteristic
231#2378C2×C14911yescharacteristic, complemented
232#1964C2×C14911yescharacteristic
233#1510C2×C14911yescharacteristic
234#1508C2×C14911yescharacteristic, complemented
235#1305C2×C14911yescharacteristic, complemented
236#1284C2×C14911yescharacteristic, complemented
237C2×C22⋊Q8C22×C14911yescharacteristic
238C2×#121C22×C14911yescharacteristic
239#484C4×C14912yescomplemented
240#480—21no—
241#468—22no—
242#450C4×C14912yescomplemented
243#448—21no—
244C2×#99—21no—
245C2×#99—21no—
246#407C22×C14911yescharacteristic
247#407C22×C14911yescharacteristic
248#391—21no—
249#389—21no—
250#388—21no—
251#388—21no—
252#387—21no—
253#387—21no—
254#381C22×C14911yescharacteristic
255#380C22×C14911yescharacteristic
256C4×C22⋊C4C22×C14911yescharacteristic
257#328—22no—
258#327—21no—
259#327—21no—
260C22×Q8D4×C14911yescharacteristic
261C22×D4—21no—
262C22×D4C2×C4×C14911yescharacteristic
263C23×C4C23×C14911yescharacteristic
264C2×SD16—22no—
265C2×M16—21no—
266C2×M16—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8C2×C4×C14912yes—
270C22⋊Q8D4×C14912yes—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4C2×C4×C14911yescharacteristic
280C2×C4⋊C4D4×C14911yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4D4×C14911yescharacteristic
286C2×C22⋊C4D4×C14911yescharacteristic
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290#107—22no—
291#103—22no—
292#102—22no—
293#99—42no—
294#99—42no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8C2×C4×C14912yes—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95D4×C14911yescharacteristic
307#95D4×C14911yescharacteristic
308C24—21no—
309C24C2×D4×C14911yescharacteristic
310C2×Q8—21no—
311C2×Q8—81no—
312C2×Q8C22⋊C4×C14912yes—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4C22×C4×C14911yescharacteristic
332C22×C4C2×D4×C14911yescharacteristic
333C22×C4C2×D4×C14911yescharacteristic
334C22×C4C2×D4×C14911yescharacteristic
335C22×C4#41×C14911yescharacteristic
336C22×C4#41×C14911yescharacteristic
337SD16—82no—
338M16—81no—
339M16—81no—
340C2×C8—22no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—81no—
348C4⋊C4—81no—
349C4⋊C4—81no—
350C4⋊C4C22⋊C4×C14912yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—81no—
360C42—81no—
361C42—81no—
362C42—81no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×D4×C14911yescharacteristic
373C23#120×C14911yescharacteristic
374C23#121×C14911yescharacteristic
375Q8—42no—
376Q8—81no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C14911yescharacteristic
414C2×C4C4×D4×C14911yescharacteristic
415C2×C4#121×C14911yescharacteristic
416C2×C4#123×C14911yescharacteristic
417C8—42no—
418C8—81no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22#386×C14911yescharacteristic
435C22#453×C14911yescharacteristic
436C22#454×C14911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—82no—
448C4—81no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2#1883×C14911yescharacteristic
455C2#1905×C14911yescharacteristic
456C2#1913×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#386
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC2×#121×C149C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #2378×C149C2semidirect
5. #1508×C149C2semidirect
6. #1305×C149C2semidirect
7. #1284×C149C2semidirect
10. #484×C149C4semidirect
13. #450×C149C4semidirect
228. #9344C149direct (N × H)
229. C149#9344direct (N × H)
231. #2378C2×C149semidirect
234. #1508C2×C149semidirect
235. #1305C2×C149semidirect
236. #1284C2×C149semidirect
239. #484C4×C149semidirect
242. #450C4×C149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3193×C1492
#2378×C1492
#1964×C1492
#1510×C1492
#1508×C1492
#1305×C1492
#1284×C1492
#9344149